In Example 12.5, show that the dimensionless hoop stress around the boundary of the hole is given

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In Example 12.5, show that the dimensionless hoop stress around the boundary of the hole is given by:

Je e Exqa/k For the cases m = (1 +m)[(1 +m+ m) sino - msin30] (1-2m cos20+ m) = 0, 1/2, +1, plot and compare

Data from example 12.5


Similar to the previous example, we now investigate the localized thermal stresses around a traction- free

1 I I I 1 I 1 1 I I 1 I 1 T b ------- I6X 19 1 I I 1 " 1

As discussed in Chapter 10, conformal mapping provides a very useful tool for this type of problem, and the

Again, this temperature field creates a dislocation in the displacement. Following similar steps as in Eqs.

p de  = Eaqa 2kh(0)' Using relations (10.7.5), the stresses in the C-plane become Eaqa -P(p + m) [p - p (1 +

with h(0) = [p* - 2p cos20 + 1]. On the surface of the crack (p = 1), the hoop stress becomes Je (1,0) Exqa 3

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